The cross sections for K-shell ionization by charged particle impact

The single ionization of inner-shell electrons by the impact of charged particles is one of the fundamental processes, which is being persistently investigated during last decades. In recent works [1-3], we have deduced the universal scaling laws for differential and total cross sections of the single K-shell ionization by electron and positron impact within the entire non-relativistic energy domain. In paper [4], we have extended the previous formulas on the case of relativistic projectiles. The study is performed to leading orders of QED perturbation theory with respect to the small parameters 1/Z andαZ , whereα is the fine-structure constant. Since it is assumed that αZ ≪ 1 and Z ≫ 1, the results turn out to be applicable for a wide family of atomic targets (both for multicharged ions and neutral atoms) with moderate values of nuclear charge numbers Z . Let us consider the inelastic electron scattering on a hydrogen-like ion, which results in the ionization of a Kshell bound electron. The multicharged ion in the ground state is characterized by the Coulomb ionization potential I = η/(2m), where η = mαZ is the average momentum of the bound electron and m is the electron mass (~ = 1, c = 1). An incident electron is characterized by the energy E and the asymptotic momentum p, which are related via E = p + m. The relativistic domain implies that Ekin & m, where Ekin = E −m denotes the kinetic energy. The final expression for the total K-shell ionization cross section σ K is given by two-fold integral, which can be easily calculated numerically. In Table 1, we present the results for σ K in the case of multicharged ions. Although the formulas obtained in work [4] are not expected to be applicable for heavy targets, the agreement of the theoretical predictions with the experimental data appears to be remarkably good. If the nuclear charge number Z is not too high, then the total cross section is given by the analytical formula [4]